Toyota Celica 2000-2006 Troubleshooting Guide
" So you could not find what seem to be the noise that comes from your vehicle "
Most common issue is could be your sway bar links. Check the sway bar links if it is losing. If does, use the tool to tie it up.
Check the sway bar links if they are rusted. If the metal looks very weak and decaying then it's probably rusted.
Use the rust spray cleaner to clean them. Check if the join is dried out. Put more Grease into the join to prevent it from getting damage.
Most common problem of the sway bar links is because that the car is old. After you had done all these guides above but the noise still does not go away then it is probably the time to replace a new one.
Check to see if the sway bar links are broken in half or have crakes or bends in it.